kurtosis parameters, although the model may be applied more generally to the parameters of any population distribution with up to four distribution parameters, and can be generalized to more than four distribution parameters. where μ, σ, ν, τ and are vectors of length , is a parameter vector of length , is a fixed known design matrix of order and is a smooth non-parametric function of explanatory variable , and . For centile estimation the WHO Multicentre Growth Reference Study Group have recommended GAMLSS and the Box–Cox power exponential (BCPE) distributions for the construction of the WHO Child Growth Standards. What distributions can be used The form of the distribution assumed for the response variable y, is very general. For example, an implementation of GAMLSS in R has around 100 different distributions available. Such implementations also allow use of truncated distributions and censored (or interval) response variables. References Further reading Cole, T. J., Stanojevic, S., Stocks, J., Coates, A. L., Hankinson, J. L., Wade, A. M. (2009), "Age- and size-related reference ranges: A case study of spirometry through childhood and adulthood", Statistics in Medicine, 28(5), 880–898.Link Fenske, N., Fahrmeir, L., Rzehak, P., Hohle, M. (25 September 2008), "Detection of risk factors for obesity in early childhood with quantile regression methods for longitudinal data", Department of Statistics: Technical Reports, No.38 Link Hudson, I. L., Kim, S. W., Keatley, M. R. (2010), "Climatic Influences on the Flowering Phenology of Four Eucalypts: A GAMLSS Approach Phenological Research". In Phenological Research, Irene L. Hudson and Marie R. Keatley (eds), Springer Netherlands Link Hudson, I. L., Rea, A., Dalrymple, M. L., Eilers, P. H. C. (2008), "Climate impacts on sudden infant death syndrome: a GAMLSS approach", Proceedings of the 23rd international workshop on statistical modelling pp. 277–280. Link Serinaldi, F., Villarini, G., Smith, J. A., Krajewski, W. F. (2008), "Change-Point and Trend Analysis on Annual Maximum Discharge in Continental United States", American Geophysical Union Fall Meeting 2008, abstract #H21A-0803* External links GAMLSS official website gamlss.org GAMLSS manual (downloadable) Distribution tables in GAMLSS The GAMLSS packages reference card (downloadable) The booklet for the Utrecht short course on GAMLSS (downloadable) R packages for GAMLSS on CRAN Additive model for location, scale and shape Semi-parametric models